论文标题
直接总和下的本地幽灵系列的斜率不变
The slope-invariant of local ghost series under direct sum
论文作者
论文摘要
幽灵猜想首先是由[BP-1，BP-2]中的Bergdall和Pollack提供的，以研究模块化形式的空间的上坡，到目前为止，这些空间已经带来了许多重要的结果。在[LTXZ-1，LTXZ-2]中，Liu-truong-Xiao-Zhao解决了这种猜想的本地版本。 在当前的论文中，我们证明了一系列本地幽灵系列的必要条件，以使他们的产品具有与幽灵系列相同的牛顿多边形，从其相关模块的直接总和。这回答了[BP2，LTXZ-1]中提出的一个常见问题。
The ghost conjecture is first provided by Bergdall and Pollack in [BP-1,BP-2] to study the Up-slopes of spaces of modular forms, which, so far, has already brought plenty of important results. The local version of this conjecture under genericity condition has been solved by Liu-Truong-Xiao-Zhao in [LTXZ-1, LTXZ-2]. In the current paper, we prove a necessary and sufficient condition for a sequence of local ghost series to satisfy that their product has the same Newton polygon to the ghost series build from the direct sum of their associated modules. That answers a common question asked in both [BP2,LTXZ-1].
